No paradox becasue of 3 things:

1. Unfathomably huge universe
2. TIme scales - billions of years
3. Realtively slow max speed of travel / information propagation

For example, consider "someone someplace else" detecting earth. How long have we done anything that would be detectable as a sign of intelligent life? Lets be really genererous and say 500 years. Well the universe is about 13 Billion years old, so we would only have been detectable in a teeny tiny fraction of the age of the universe. And the chances of being detected are further dwarfed by the extremely low chances of some detector looking in our direction is that same teeny tiny window of time. And where would these detectors have to be? If we've been detectable for 500 years then the detectors would have to within a 500 light year bubble around earth. A teeny tiny fraction of our own galaxy. Forget other galaxies (our closest neighbor galaxy is about 25000 light year away which means they could not detect us for another 24,500 years). And then there is that part of the universe we will never see at all because it is moving away from us faster than light speed (god knows how big that is). My point is that the chances of any contact (or even detection) are virtually zero. The universe is probably full of life. All of it alone and isolated. Forever.